TSTP Solution File: NUM500+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM500+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 : n023.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 10:38:07 EDT 2023
% Result : Theorem 0.50s 0.63s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 46 ( 5 unt; 28 typ; 0 def)
% Number of atoms : 146 ( 71 equ)
% Maximal formula atoms : 73 ( 8 avg)
% Number of connectives : 193 ( 65 ~; 87 |; 38 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 19 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn; 6 !; 7 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_1: $i > $i ).
tff(decl_49,type,
esk13_1: $i > $i ).
fof(m__,conjecture,
? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(c_0_4,negated_conjecture,
~ ? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,negated_conjecture,
! [X103,X104] :
( ( aNaturalNumber0(esk12_1(X103))
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( aNaturalNumber0(esk13_1(X103))
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( X103 = sdtasdt0(esk12_1(X103),esk13_1(X103))
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( doDivides0(esk12_1(X103),X103)
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( esk12_1(X103) != sz10
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( esk12_1(X103) != X103
| X103 = sz00
| X103 = sz10
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( ~ isPrime0(X103)
| ~ aNaturalNumber0(X104)
| xk != sdtasdt0(X103,X104)
| ~ aNaturalNumber0(X103) )
& ( aNaturalNumber0(esk12_1(X103))
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( aNaturalNumber0(esk13_1(X103))
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( X103 = sdtasdt0(esk12_1(X103),esk13_1(X103))
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( doDivides0(esk12_1(X103),X103)
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( esk12_1(X103) != sz10
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( esk12_1(X103) != X103
| X103 = sz00
| X103 = sz10
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) )
& ( ~ isPrime0(X103)
| ~ doDivides0(X103,xk)
| ~ aNaturalNumber0(X103) ) ),
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_4])])])])]) ).
fof(c_0_6,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])])])]) ).
fof(c_0_7,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_8,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_11,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( ~ isPrime0(esk4_1(xk))
| ~ aNaturalNumber0(esk4_1(xk)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]),c_0_12]) ).
cnf(c_0_14,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
~ isPrime0(esk4_1(xk)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10])]),c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10])]),c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n023.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 : Fri Aug 25 14:44:27 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.50/0.58 start to proof: theBenchmark
% 0.50/0.63 % Version : CSE_E---1.5
% 0.50/0.63 % Problem : theBenchmark.p
% 0.50/0.63 % Proof found
% 0.50/0.63 % SZS status Theorem for theBenchmark.p
% 0.50/0.63 % SZS output start Proof
% See solution above
% 0.54/0.64 % Total time : 0.046000 s
% 0.54/0.64 % SZS output end Proof
% 0.54/0.64 % Total time : 0.050000 s
%------------------------------------------------------------------------------