TSTP Solution File: NUM699^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% 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 10:45:16 EDT 2024
% Result : Theorem 2.64s 1.63s
% Output : Refutation 2.64s
% 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 : 71 ( 8 ~; 3 |; 0 &; 58 @)
% ( 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(lessis_type,type,
lessis: nat > nat > $o ).
thf(suc_type,type,
suc: nat > nat ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(n_1_type,type,
n_1: nat ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( less @ B @ A )
=> ( lessis @ ( pl @ B @ n_1 ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz25b) ).
thf(8,plain,
! [A: nat,B: nat] :
( ( less @ B @ A )
=> ( lessis @ ( pl @ B @ n_1 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ A )
| ( lessis @ ( pl @ B @ n_1 ) @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(5,axiom,
! [A: nat] :
( ( pl @ A @ n_1 )
= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4a) ).
thf(10,plain,
! [A: nat] :
( ( pl @ A @ n_1 )
= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,plain,
! [A: nat] :
( ( pl @ A @ n_1 )
= ( suc @ A ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: nat] :
( ( pl @ A @ n_1 )
= ( suc @ A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(13,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ A )
| ( lessis @ ( suc @ B ) @ A ) ),
inference(rewrite,[status(thm)],[9,12]) ).
thf(1,conjecture,
lessis @ ( suc @ y ) @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz25c) ).
thf(2,negated_conjecture,
~ ( lessis @ ( suc @ y ) @ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( lessis @ ( suc @ y ) @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
! [B: nat,A: nat] :
( ~ ( less @ B @ A )
| ( ( lessis @ ( suc @ B ) @ A )
!= ( lessis @ ( suc @ y ) @ x ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(15,plain,
~ ( less @ y @ x ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(3,axiom,
less @ y @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(7,plain,
less @ y @ 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
% 0.06/0.12 % Problem : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n022.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 19:41:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.10/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.05 % [INFO] Parsing done (122ms).
% 1.24/1.06 % [INFO] Running in sequential loop mode.
% 1.69/1.27 % [INFO] nitpick registered as external prover.
% 1.69/1.28 % [INFO] Scanning for conjecture ...
% 1.69/1.32 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.97/1.34 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.97/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.35 % [INFO] Type checking passed.
% 1.97/1.36 % [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 ...
% 2.64/1.63 % [INFO] Killing All external provers ...
% 2.64/1.63 % Time passed: 1093ms (effective reasoning time: 569ms)
% 2.64/1.63 % 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)>
% 2.64/1.63 % Axioms used in derivation (3): satz25b, satz4a, l
% 2.64/1.63 % No. of inferences in proof: 17
% 2.64/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1093 ms resp. 569 ms w/o parsing
% 2.64/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.64/1.66 % [INFO] Killing All external provers ...
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