TSTP Solution File: NUM482+3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 : Tue May 7 10:44:27 EDT 2024
% Result : Theorem 11.93s 3.25s
% Output : Refutation 11.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 122 ( 43 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 260 ( 43 ~; 42 |; 37 &; 127 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 ^ 22 !; 12 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(doDivides0_type,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(isPrime0_type,type,
isPrime0: $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(xk_type,type,
xk: $i ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(36,axiom,
aNaturalNumber0 @ xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
thf(223,plain,
aNaturalNumber0 @ xk,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(39,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(232,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(233,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz10 )
= A ) ),
inference(cnf,[status(esa)],[232]) ).
thf(235,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(1969,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz10 )
= A )
| ( ( aNaturalNumber0 @ xk )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[223,235]) ).
thf(1970,plain,
( ( sdtasdt0 @ xk @ sz10 )
= xk ),
inference(pattern_uni,[status(thm)],[1969:[bind(A,$thf( xk ))]]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) ) )
=> ( ( A = sz10 )
| ( A = xk ) ) )
& ( isPrime0 @ xk ) )
=> ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) )
& ( ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( A
= ( sdtasdt0 @ B @ C ) ) )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) )
| ( isPrime0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) ) )
=> ( ( A = sz10 )
| ( A = xk ) ) )
& ( isPrime0 @ xk ) )
=> ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) )
& ( ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( A
= ( sdtasdt0 @ B @ C ) ) )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) )
| ( isPrime0 @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ( ( ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) ) )
=> ( ( A = sz10 )
| ( A = xk ) ) )
& ( isPrime0 @ xk ) )
=> ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xk
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xk ) )
& ( ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( A
= ( sdtasdt0 @ B @ C ) ) )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) )
| ( isPrime0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( xk
!= ( sdtasdt0 @ A @ B ) )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= xk )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
!= xk )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sk1 @ A ) ),
inference(simp,[status(thm)],[58]) ).
thf(2029,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( sk1 @ A )
| ( ( sdtasdt0 @ xk @ sz10 )
!= ( sdtasdt0 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1970,59]) ).
thf(2030,plain,
( ~ ( aNaturalNumber0 @ xk )
| ~ ( aNaturalNumber0 @ sz10 )
| ~ ( sk1 @ xk ) ),
inference(pattern_uni,[status(thm)],[2029:[bind(A,$thf( xk )),bind(B,$thf( sz10 ))]]) ).
thf(6,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(85,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(87,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[85]) ).
thf(52,plain,
isPrime0 @ xk,
inference(cnf,[status(esa)],[43]) ).
thf(48,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sk1 @ A )
| ~ ( isPrime0 @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(64,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sk1 @ A )
| ~ ( isPrime0 @ A ) ),
inference(simp,[status(thm)],[48]) ).
thf(275,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sk1 @ A )
| ( ( isPrime0 @ xk )
!= ( isPrime0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52,64]) ).
thf(276,plain,
( ~ ( aNaturalNumber0 @ xk )
| ( sk1 @ xk ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( xk ))]]) ).
thf(314,plain,
( ~ $true
| ( sk1 @ xk ) ),
inference(rewrite,[status(thm)],[276,223]) ).
thf(315,plain,
sk1 @ xk,
inference(simp,[status(thm)],[314]) ).
thf(2524,plain,
( ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2030,87,315,223]) ).
thf(2525,plain,
$false,
inference(simp,[status(thm)],[2524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 19:26:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (140ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 1.86/1.20 % [INFO] nitpick registered as external prover.
% 1.86/1.20 % [INFO] Scanning for conjecture ...
% 1.96/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.96/1.30 % [INFO] Found a conjecture and 40 axioms. Running axiom selection ...
% 2.16/1.35 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.38/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.41 % [INFO] Type checking passed.
% 2.38/1.41 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.93/3.24 % [INFO] Killing All external provers ...
% 11.93/3.25 % Time passed: 2727ms (effective reasoning time: 2249ms)
% 11.93/3.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.93/3.25 % Axioms used in derivation (3): m__1716, m_MulUnit, mSortsC_01
% 11.93/3.25 % No. of inferences in proof: 28
% 11.93/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2727 ms resp. 2249 ms w/o parsing
% 11.93/3.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.93/3.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------