TSTP Solution File: COL006-6 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL006-6 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 07:29:12 EDT 2024
% Result : Unsatisfiable 3.03s 1.63s
% Output : Refutation 3.03s
% 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 : 130 ( 2 ~; 0 |; 0 &; 128 @)
% ( 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(s_type,type,
s: $i ).
thf(k_type,type,
k: $i ).
thf(1,negated_conjecture,
( ( apply @ strong_fixed_point @ fixed_pt )
!= ( apply @ fixed_pt @ ( apply @ strong_fixed_point @ fixed_pt ) ) ),
file('/export/starexec/sandbox/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 @ s @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
= ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( apply @ ( apply @ k @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( apply @ ( apply @ k @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( strong_fixed_point
= ( apply @ ( apply @ s @ ( apply @ k @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ k ) @ k ) ) @ ( apply @ ( apply @ s @ k ) @ k ) ) ) ) @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ ( apply @ k @ s ) ) @ k ) ) @ ( apply @ k @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ k ) @ k ) ) @ ( apply @ ( apply @ s @ k ) @ k ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
thf(12,plain,
( strong_fixed_point
= ( apply @ ( apply @ s @ ( apply @ k @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ k ) @ k ) ) @ ( apply @ ( apply @ s @ k ) @ k ) ) ) ) @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ ( apply @ k @ s ) ) @ k ) ) @ ( apply @ k @ ( apply @ ( apply @ s @ ( apply @ ( apply @ s @ k ) @ k ) ) @ ( apply @ ( apply @ s @ k ) @ k ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
$false,
inference(cvc4,[status(thm)],[5,8,10,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL006-6 : TPTP v8.1.2. Released v2.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 14:04:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.85/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.90 % [INFO] Parsing done (102ms).
% 1.11/0.91 % [INFO] Running in sequential loop mode.
% 1.49/1.11 % [INFO] eprover registered as external prover.
% 1.49/1.12 % [INFO] cvc4 registered as external prover.
% 1.49/1.12 % [INFO] Scanning for conjecture ...
% 1.73/1.16 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.73/1.18 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.73/1.19 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.20 % [INFO] Type checking passed.
% 1.83/1.20 % [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 ...
% 3.03/1.62 % External prover 'cvc4' found a proof!
% 3.03/1.62 % [INFO] Killing All external provers ...
% 3.03/1.63 % Time passed: 1108ms (effective reasoning time: 710ms)
% 3.03/1.63 % 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)>
% 3.03/1.63 % Axioms used in derivation (3): s_definition, k_definition, strong_fixed_point
% 3.03/1.63 % No. of inferences in proof: 9
% 3.03/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1108 ms resp. 710 ms w/o parsing
% 3.03/1.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.03/1.67 % [INFO] Killing All external provers ...
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