TSTP Solution File: SWW469+1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : Mon Jun 24 18:22:37 EDT 2024
% Result : Theorem 2.96s 2.10s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 42 ( 10 ~; 0 |; 7 &; 16 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 ^ 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_state_type,type,
is_state: $i > $o ).
thf(undefined_state_type,type,
undefined_state: $i > $i ).
thf(state_type,type,
state: $i ).
thf(hoare_165779456gleton_type,type,
hoare_165779456gleton: $o ).
thf(induct_false_type,type,
induct_false: $o ).
thf(induct_true_type,type,
induct_true: $o ).
thf(4,axiom,
( hoare_165779456gleton
<=> ? [A: $i,B: $i] :
( ( is_state @ A )
& ( is_state @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(14,plain,
( ( hoare_165779456gleton
=> ? [A: $i,B: $i] :
( ( is_state @ A )
& ( is_state @ B )
& ( A != B ) ) )
& ( ? [A: $i,B: $i] :
( ( is_state @ A )
& ( is_state @ B )
& ( A != B ) )
=> hoare_165779456gleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i] :
( ( is_state @ A )
=> ~ ! [B: $i] :
( ( is_state @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( is_state @ A )
=> ~ ! [B: $i] :
( ( is_state @ B )
=> ( B = A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i] :
( ( is_state @ A )
=> ~ ! [B: $i] :
( ( is_state @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
is_state @ ( undefined_state @ state ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Ostate) ).
thf(13,plain,
is_state @ ( undefined_state @ state ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
~ induct_false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_induct__false__def) ).
thf(22,plain,
~ induct_false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
hoare_165779456gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(26,plain,
hoare_165779456gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_induct__trueI) ).
thf(24,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_induct__true__def) ).
thf(25,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[14,9,13,22,26,24,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW469+1 : TPTP v8.2.0. Released v5.3.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Jun 19 04:48:40 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.99/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.13 % [INFO] Parsing done (154ms).
% 1.33/1.14 % [INFO] Running in sequential loop mode.
% 1.80/1.52 % [INFO] eprover registered as external prover.
% 1.80/1.53 % [INFO] Scanning for conjecture ...
% 2.05/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.05/1.64 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.21/1.66 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.66 % [INFO] Type checking passed.
% 2.21/1.66 % [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 ...
% 2.96/2.10 % External prover 'e' found a proof!
% 2.96/2.10 % [INFO] Killing All external provers ...
% 2.96/2.10 % Time passed: 1610ms (effective reasoning time: 950ms)
% 2.96/2.10 % 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)>
% 2.96/2.10 % Axioms used in derivation (6): gsy_c_HOL_Oundefined_000tc__Com__Ostate, fact_0_state__not__singleton__def, fact_3_induct__true__def, fact_1_induct__false__def, conj_0, fact_2_induct__trueI
% 2.96/2.10 % No. of inferences in proof: 16
% 2.96/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1610 ms resp. 950 ms w/o parsing
% 3.09/2.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.09/2.14 % [INFO] Killing All external provers ...
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