TSTP Solution File: DAT187^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : DAT187^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 10:30:13 EDT 2024
% Result : Theorem 39.46s 7.55s
% Output : Refutation 39.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 30 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 62 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 227 ( 15 ~; 6 |; 3 &; 203 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 18 ( 0 ^ 11 !; 3 ?; 18 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(coinductive_lappend_type,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2435255213lllsts_type,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: set @ ( coinductive_llist @ a ) ).
thf(r_type,type,
r: coinductive_llist @ a ).
thf(t_type,type,
t: coinductive_llist @ a ).
thf(u_type,type,
u: coinductive_llist @ a ).
thf(v_type,type,
v: coinductive_llist @ a ).
thf(114,axiom,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062) ).
thf(584,plain,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(585,plain,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) ) ),
inference(lifteq,[status(thm)],[584]) ).
thf(205,axiom,
member @ ( coinductive_llist @ a ) @ t @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tP) ).
thf(879,plain,
member @ ( coinductive_llist @ a ) @ t @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1,conjecture,
? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(281,plain,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(282,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ~ ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(cnf,[status(esa)],[281]) ).
thf(1793,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( member @ ( coinductive_llist @ a ) @ t @ p )
!= ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ) ),
inference(paramod_ordered,[status(thm)],[879,282]) ).
thf(1797,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( t
!= ( coinductive_lappend @ a @ r @ A ) )
| ( p != p ) ),
inference(simp,[status(thm)],[1793]) ).
thf(1814,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( t
!= ( coinductive_lappend @ a @ r @ A ) ) ),
inference(simp,[status(thm)],[1797]) ).
thf(2631,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ v ) )
!= ( coinductive_lappend @ a @ r @ A ) ) ),
inference(paramod_ordered,[status(thm)],[585,1814]) ).
thf(2632,plain,
~ ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ u @ v ) @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) ),
inference(pattern_uni,[status(thm)],[2631:[bind(A,$thf( coinductive_lappend @ a @ u @ v ))]]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_alllsts__UNIV) ).
thf(727,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(728,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(cnf,[status(esa)],[727]) ).
thf(3416,plain,
~ $true,
inference(rewrite,[status(thm)],[2632,728]) ).
thf(3417,plain,
$false,
inference(simp,[status(thm)],[3416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT187^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 18:45:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.99/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.12 % [INFO] Parsing done (268ms).
% 1.78/1.13 % [INFO] Running in sequential loop mode.
% 2.72/1.34 % [INFO] nitpick registered as external prover.
% 2.72/1.35 % [INFO] Scanning for conjecture ...
% 3.14/1.46 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 3.52/1.58 % [INFO] Axiom selection finished. Selected 278 axioms (removed 1 axioms).
% 4.35/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 4.35/1.83 % [INFO] Type checking passed.
% 4.35/1.83 % [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 ...
% 39.46/7.54 % [INFO] Killing All external provers ...
% 39.46/7.55 % Time passed: 7025ms (effective reasoning time: 6418ms)
% 39.46/7.55 % 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)>
% 39.46/7.55 % Axioms used in derivation (3): fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062, fact_0_tP, fact_5_alllsts__UNIV
% 39.46/7.55 % No. of inferences in proof: 19
% 39.46/7.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7025 ms resp. 6418 ms w/o parsing
% 39.46/7.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.46/7.58 % [INFO] Killing All external provers ...
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