TSTP Solution File: ANA003-4 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 10:08:43 EDT 2023
% Result : Unsatisfiable 2.67s 1.57s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 39 ( 3 unt; 14 typ; 0 def)
% Number of atoms : 55 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 274 ( 24 ~; 30 |; 0 &; 220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(absolute_type,type,
absolute: $i > $i ).
thf(f_type,type,
f: $i > $i ).
thf(xs_type,type,
xs: $i > $i ).
thf(negate_type,type,
negate: $i > $i ).
thf(a_real_number_type,type,
a_real_number: $i ).
thf(g_type,type,
g: $i > $i ).
thf(epsilon_0_type,type,
epsilon_0: $i ).
thf(minimum_type,type,
minimum: $i > $i > $i ).
thf(half_type,type,
half: $i > $i ).
thf(delta_1_type,type,
delta_1: $i > $i ).
thf(delta_2_type,type,
delta_2: $i > $i ).
thf(7,axiom,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ A ) @ n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(25,plain,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( delta_1 @ A ) @ n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ B @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ A ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ B ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ B @ ( negate @ a_real_number ) ) ) @ ( delta_1 @ A ) )
| ( less_or_equal @ ( absolute @ ( add @ ( f @ B ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( add @ ( absolute @ ( add @ ( f @ ( xs @ A ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ ( absolute @ ( add @ ( g @ ( xs @ A ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_2) ).
thf(13,plain,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( add @ ( absolute @ ( add @ ( f @ ( xs @ A ) ) @ ( negate @ ( f @ a_real_number ) ) ) ) @ ( absolute @ ( add @ ( g @ ( xs @ A ) ) @ ( negate @ ( g @ a_real_number ) ) ) ) ) @ epsilon_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( minimum @ B @ C ) )
| ( less_or_equal @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum7) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( minimum @ B @ C ) )
| ( less_or_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ A ) @ n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(27,plain,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( delta_2 @ A ) @ n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ A ) @ ( negate @ a_real_number ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(35,plain,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ( less_or_equal @ ( absolute @ ( add @ ( xs @ A ) @ ( negate @ a_real_number ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ B @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ A ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ B ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( absolute @ ( add @ B @ ( negate @ a_real_number ) ) ) @ ( delta_2 @ A ) )
| ( less_or_equal @ ( absolute @ ( add @ ( g @ B ) @ ( negate @ ( g @ a_real_number ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( half @ A ) @ n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
thf(23,plain,
! [A: $i] :
( ( less_or_equal @ A @ n0 )
| ~ ( less_or_equal @ ( half @ A ) @ n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ( less_or_equal @ B @ n0 )
| ~ ( less_or_equal @ ( minimum @ A @ B ) @ n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ n0 )
| ( less_or_equal @ B @ n0 )
| ~ ( less_or_equal @ ( minimum @ A @ B ) @ n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( minimum @ B @ C ) )
| ( less_or_equal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum3) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( minimum @ B @ C ) )
| ( less_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( half @ B ) )
| ~ ( less_or_equal @ C @ ( half @ B ) )
| ( less_or_equal @ ( add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_or_equal @ A @ ( half @ B ) )
| ~ ( less_or_equal @ C @ ( half @ B ) )
| ( less_or_equal @ ( add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
~ ( less_or_equal @ epsilon_0 @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(33,plain,
~ ( less_or_equal @ epsilon_0 @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[25,29,13,17,27,35,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n020.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 : Thu May 18 17:53:33 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (116ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.50/1.17 % [INFO] eprover registered as external prover.
% 1.50/1.17 % [INFO] cvc4 registered as external prover.
% 1.50/1.18 % [INFO] Scanning for conjecture ...
% 1.78/1.23 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.84/1.25 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.84/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.27 % [INFO] Type checking passed.
% 1.84/1.27 % [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 ...
% 2.67/1.56 % External prover 'e' found a proof!
% 2.67/1.56 % [INFO] Killing All external provers ...
% 2.67/1.57 % Time passed: 1029ms (effective reasoning time: 579ms)
% 2.67/1.57 % 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)>
% 2.67/1.57 % Axioms used in derivation (11): zero_and_half, clause_2, clause_1, minimum7, clause_4, minimum3, clause_6, less_or_equal_sum_of_halves, clause_3, minimum9, clause_5
% 2.67/1.57 % No. of inferences in proof: 25
% 2.67/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1029 ms resp. 579 ms w/o parsing
% 2.67/1.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------