TSTP Solution File: NUM701^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM701^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 10:45:17 EDT 2024
% Result : Theorem 2.49s 1.61s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 24 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 8 ~; 3 |; 0 &; 57 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 ^ 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(y_type,type,
y: nat ).
thf(less_type,type,
less: nat > nat > $o ).
thf(suc_type,type,
suc: nat > nat ).
thf(lessis_type,type,
lessis: nat > nat > $o ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(n_1_type,type,
n_1: nat ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( less @ B @ ( pl @ A @ n_1 ) )
=> ( lessis @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz26) ).
thf(8,plain,
! [A: nat,B: nat] :
( ( less @ B @ ( pl @ A @ n_1 ) )
=> ( lessis @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ ( pl @ A @ n_1 ) )
| ( lessis @ B @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(5,axiom,
! [A: nat] :
( ( suc @ A )
= ( pl @ A @ n_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4e) ).
thf(10,plain,
! [A: nat] :
( ( suc @ A )
= ( pl @ A @ n_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,plain,
! [A: nat] :
( ( suc @ A )
= ( pl @ A @ n_1 ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: nat] :
( ( pl @ A @ n_1 )
= ( suc @ A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(13,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ ( suc @ A ) )
| ( lessis @ B @ A ) ),
inference(rewrite,[status(thm)],[9,12]) ).
thf(1,conjecture,
lessis @ y @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz26a) ).
thf(2,negated_conjecture,
~ ( lessis @ y @ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( lessis @ y @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ ( suc @ A ) )
| ( ( lessis @ B @ A )
!= ( lessis @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(15,plain,
~ ( less @ y @ ( suc @ x ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(3,axiom,
less @ y @ ( suc @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(7,plain,
less @ y @ ( suc @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
~ $true,
inference(rewrite,[status(thm)],[15,7]) ).
thf(19,plain,
$false,
inference(simp,[status(thm)],[18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM701^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n027.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 19:38:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.02 % [INFO] Parsing done (117ms).
% 1.26/1.02 % [INFO] Running in sequential loop mode.
% 1.73/1.25 % [INFO] nitpick registered as external prover.
% 1.73/1.25 % [INFO] Scanning for conjecture ...
% 1.82/1.29 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.82/1.31 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.82/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.82/1.33 % [INFO] Type checking passed.
% 2.00/1.33 % [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 ...
% 2.49/1.61 % [INFO] Killing All external provers ...
% 2.49/1.61 % Time passed: 1045ms (effective reasoning time: 582ms)
% 2.49/1.61 % 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)>
% 2.49/1.61 % Axioms used in derivation (3): satz26, satz4e, l
% 2.49/1.61 % No. of inferences in proof: 17
% 2.49/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1045 ms resp. 582 ms w/o parsing
% 2.49/1.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.49/1.64 % [INFO] Killing All external provers ...
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