TSTP Solution File: NUM423+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM423+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 : n003.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 10:37:17 EDT 2023
% Result : Theorem 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 102 ( 26 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 123 ( 50 ~; 48 |; 18 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn; 20 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aInteger0: $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,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
xa: $i ).
tff(decl_31,type,
xq: $i ).
tff(decl_32,type,
esk1_2: ( $i * $i ) > $i ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(m__671,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(c_0_8,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_9,plain,
! [X34,X35,X36] :
( ( ~ sdteqdtlpzmzozddtrp0(X34,X35,X36)
| aDivisorOf0(X36,sdtpldt0(X34,smndt0(X35)))
| ~ aInteger0(X34)
| ~ aInteger0(X35)
| ~ aInteger0(X36)
| X36 = sz00 )
& ( ~ aDivisorOf0(X36,sdtpldt0(X34,smndt0(X35)))
| sdteqdtlpzmzozddtrp0(X34,X35,X36)
| ~ aInteger0(X34)
| ~ aInteger0(X35)
| ~ aInteger0(X36)
| X36 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
fof(c_0_10,plain,
! [X29,X30,X32,X33] :
( ( aInteger0(X30)
| ~ aDivisorOf0(X30,X29)
| ~ aInteger0(X29) )
& ( X30 != sz00
| ~ aDivisorOf0(X30,X29)
| ~ aInteger0(X29) )
& ( aInteger0(esk1_2(X29,X30))
| ~ aDivisorOf0(X30,X29)
| ~ aInteger0(X29) )
& ( sdtasdt0(X30,esk1_2(X29,X30)) = X29
| ~ aDivisorOf0(X30,X29)
| ~ aInteger0(X29) )
& ( ~ aInteger0(X32)
| X32 = sz00
| ~ aInteger0(X33)
| sdtasdt0(X32,X33) != X29
| aDivisorOf0(X32,X29)
| ~ aInteger0(X29) ) ),
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)],[mDivisor])])])])])]) ).
fof(c_0_11,plain,
! [X7,X8] :
( ~ aInteger0(X7)
| ~ aInteger0(X8)
| aInteger0(sdtasdt0(X7,X8)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_12,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__671]) ).
cnf(c_0_15,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__671]) ).
cnf(c_0_16,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__671]) ).
fof(c_0_17,plain,
! [X15] :
( ( sdtpldt0(X15,smndt0(X15)) = sz00
| ~ aInteger0(X15) )
& ( sz00 = sdtpldt0(smndt0(X15),X15)
| ~ aInteger0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_18,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X25] :
( ( sdtasdt0(X25,sz00) = sz00
| ~ aInteger0(X25) )
& ( sz00 = sdtasdt0(sz00,X25)
| ~ aInteger0(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_21,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_22,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_26,negated_conjecture,
~ aDivisorOf0(xq,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14])]) ).
cnf(c_0_27,plain,
( X1 = sz00
| aDivisorOf0(X1,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 09:08:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.57 % Version : CSE_E---1.5
% 0.18/0.57 % Problem : theBenchmark.p
% 0.18/0.57 % Proof found
% 0.18/0.57 % SZS status Theorem for theBenchmark.p
% 0.18/0.57 % SZS output start Proof
% See solution above
% 0.18/0.57 % Total time : 0.011000 s
% 0.18/0.57 % SZS output end Proof
% 0.18/0.57 % Total time : 0.014000 s
%------------------------------------------------------------------------------