TSTP Solution File: COL003-16 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL003-16 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 07:29:10 EDT 2024
% Result : Unsatisfiable 3.78s 1.95s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 14 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 78 ( 2 ~; 0 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 ^ 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_type,type,
apply: $i > $i > $i ).
thf(strong_fixed_point_type,type,
strong_fixed_point: $i ).
thf(fixed_pt_type,type,
fixed_pt: $i ).
thf(b_type,type,
b: $i ).
thf(w_type,type,
w: $i ).
thf(1,negated_conjecture,
( ( apply @ strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ strong_fixed_point @ fixed_pt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
thf(5,plain,
( ( apply @ strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ strong_fixed_point @ fixed_pt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( apply @ ( apply @ w @ A ) @ B )
= ( apply @ ( apply @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( apply @ ( apply @ w @ A ) @ B )
= ( apply @ ( apply @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( strong_fixed_point
= ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ w ) ) @ b ) ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
thf(12,plain,
( strong_fixed_point
= ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ ( apply @ b @ ( apply @ w @ w ) ) @ w ) ) @ b ) ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(127,plain,
$false,
inference(e,[status(thm)],[5,8,10,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COL003-16 : TPTP v8.1.2. Released v2.1.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n013.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon May 6 14:04:54 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (109ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.59/1.20 % [INFO] eprover registered as external prover.
% 1.69/1.20 % [INFO] cvc4 registered as external prover.
% 1.69/1.20 % [INFO] Scanning for conjecture ...
% 1.80/1.25 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.80/1.26 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.80/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/1.27 % [INFO] Type checking passed.
% 1.80/1.28 % [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 ...
% 3.78/1.95 % External prover 'e' found a proof!
% 3.78/1.95 % [INFO] Killing All external provers ...
% 3.78/1.95 % Time passed: 1406ms (effective reasoning time: 952ms)
% 3.78/1.95 % 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)>
% 3.78/1.95 % Axioms used in derivation (3): b_definition, w_definition, strong_fixed_point
% 3.78/1.95 % No. of inferences in proof: 9
% 3.78/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1406 ms resp. 952 ms w/o parsing
% 3.78/1.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.78/1.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------