TSTP Solution File: NUM283-1.005 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Fri May 19 11:40:11 EDT 2023
% Result : Unsatisfiable 2.68s 1.53s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 20 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 25 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 12 ~; 10 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(factorial_type,type,
factorial: $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(2,axiom,
! [A: $i] : ( sum @ A @ n0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_0) ).
thf(10,plain,
! [A: $i] : ( sum @ A @ n0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( product @ D @ B @ A )
| ( product @ ( s @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( product @ D @ B @ A )
| ( product @ ( s @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] : ( product @ ( s @ n0 ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times1) ).
thf(13,plain,
! [A: $i] : ( product @ ( s @ n0 ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( factorial @ A @ B )
| ~ ( product @ ( s @ A ) @ B @ C )
| ( factorial @ ( s @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( factorial @ A @ B )
| ~ ( product @ ( s @ A ) @ B @ C )
| ( factorial @ ( s @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
factorial @ n0 @ ( s @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factorial_0) ).
thf(16,plain,
factorial @ n0 @ ( s @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ A @ ( s @ B ) @ ( s @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ A @ ( s @ B ) @ ( s @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_factorial) ).
thf(8,plain,
! [A: $i] :
~ ( factorial @ ( s @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[10,14,13,17,16,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : NUM283-1.005 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 17:39:38 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.94 % [INFO] Parsing done (110ms).
% 1.23/0.95 % [INFO] Running in sequential loop mode.
% 1.50/1.14 % [INFO] eprover registered as external prover.
% 1.50/1.15 % [INFO] cvc4 registered as external prover.
% 1.50/1.15 % [INFO] Scanning for conjecture ...
% 1.76/1.20 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.76/1.22 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.76/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.76/1.23 % [INFO] Type checking passed.
% 1.89/1.23 % [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 ...
% 2.68/1.53 % External prover 'e' found a proof!
% 2.68/1.53 % [INFO] Killing All external provers ...
% 2.68/1.53 % Time passed: 1023ms (effective reasoning time: 582ms)
% 2.68/1.53 % 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)>
% 2.68/1.53 % Axioms used in derivation (6): factorial, times1, factorial_0, add, add_0, times
% 2.68/1.53 % No. of inferences in proof: 15
% 2.68/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1023 ms resp. 582 ms w/o parsing
% 2.72/1.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.72/1.56 % [INFO] Killing All external provers ...
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