TSTP Solution File: ITP028^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n019.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 09:27:38 EDT 2024
% Result : Theorem 8.35s 2.83s
% Output : Refutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 165 ( 25 ~; 18 |; 6 &; 108 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 0 ^ 6 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1710391469_a_a_e_type,type,
set_Pr1710391469_a_a_e: $tType ).
thf(produc169085773_a_a_e_type,type,
produc169085773_a_a_e: $tType ).
thf(set_se821189730_a_a_e_type,type,
set_se821189730_a_a_e: $tType ).
thf(set_Pr2045688071_set_a_type,type,
set_Pr2045688071_set_a: $tType ).
thf(set_Pr204296108_a_a_e_type,type,
set_Pr204296108_a_a_e: $tType ).
thf(set_Pr305929312_set_a_type,type,
set_Pr305929312_set_a: $tType ).
thf(produc1691597095_set_a_type,type,
produc1691597095_set_a: $tType ).
thf(produc715398134_a_a_e_type,type,
produc715398134_a_a_e: $tType ).
thf(produc1965228714_set_a_type,type,
produc1965228714_set_a: $tType ).
thf(set_set_set_a_type,type,
set_set_set_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_a_e_type,type,
set_a_e: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(e_type,type,
e: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(produc1040928388_a_a_e_type,type,
produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).
thf(image_64240033_set_a_type,type,
image_64240033_set_a: ( produc715398134_a_a_e > set_a ) > set_Pr204296108_a_a_e > set_set_a ).
thf(member_set_a_type,type,
member_set_a: set_a > set_set_a > $o ).
thf(c_type,type,
c: set_Pr204296108_a_a_e ).
thf(a1_type,type,
a1: set_a ).
thf(a2_type,type,
a2: set_a ).
thf(a3_type,type,
a3: set_a ).
thf(thesis_type,type,
thesis: $o ).
thf(sk30_type,type,
sk30: set_a ).
thf(85,axiom,
? [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
& ( ord_less_eq_set_a @ a1 @ A )
& ( ord_less_eq_set_a @ a2 @ A )
& ( ord_less_eq_set_a @ a3 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062) ).
thf(392,plain,
? [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
& ( ord_less_eq_set_a @ a1 @ A )
& ( ord_less_eq_set_a @ a2 @ A )
& ( ord_less_eq_set_a @ a3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(396,plain,
member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
inference(cnf,[status(esa)],[392]) ).
thf(393,plain,
ord_less_eq_set_a @ a3 @ sk30,
inference(cnf,[status(esa)],[392]) ).
thf(102,axiom,
! [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ A )
=> ( ( ord_less_eq_set_a @ a2 @ A )
=> ( ( ord_less_eq_set_a @ a3 @ A )
=> thesis ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(445,plain,
! [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ A )
=> ( ( ord_less_eq_set_a @ a2 @ A )
=> ( ( ord_less_eq_set_a @ a3 @ A )
=> thesis ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(446,plain,
! [A: set_a] :
( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ ( ord_less_eq_set_a @ a1 @ A )
| ~ ( ord_less_eq_set_a @ a2 @ A )
| ~ ( ord_less_eq_set_a @ a3 @ A )
| thesis ),
inference(cnf,[status(esa)],[445]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(103,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(448,plain,
! [A: set_a] :
( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ ( ord_less_eq_set_a @ a1 @ A )
| ~ ( ord_less_eq_set_a @ a2 @ A )
| ~ ( ord_less_eq_set_a @ a3 @ A )
| $false ),
inference(rewrite,[status(thm)],[446,103]) ).
thf(449,plain,
! [A: set_a] :
( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ ( ord_less_eq_set_a @ a1 @ A )
| ~ ( ord_less_eq_set_a @ a2 @ A )
| ~ ( ord_less_eq_set_a @ a3 @ A ) ),
inference(simp,[status(thm)],[448]) ).
thf(456,plain,
! [A: set_a] :
( ~ ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ ( ord_less_eq_set_a @ a1 @ A )
| ~ ( ord_less_eq_set_a @ a2 @ A )
| ( ( ord_less_eq_set_a @ a3 @ sk30 )
!= ( ord_less_eq_set_a @ a3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[393,449]) ).
thf(457,plain,
( ~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ ( ord_less_eq_set_a @ a1 @ sk30 )
| ~ ( ord_less_eq_set_a @ a2 @ sk30 ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( sk30 ))]]) ).
thf(394,plain,
ord_less_eq_set_a @ a2 @ sk30,
inference(cnf,[status(esa)],[392]) ).
thf(395,plain,
ord_less_eq_set_a @ a1 @ sk30,
inference(cnf,[status(esa)],[392]) ).
thf(512,plain,
( ~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[457,394,395]) ).
thf(513,plain,
~ ( member_set_a @ sk30 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) ),
inference(simp,[status(thm)],[512]) ).
thf(662,plain,
$false,
inference(rewrite,[status(thm)],[396,513]) ).
thf(663,plain,
$false,
inference(simp,[status(thm)],[662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jun 19 00:09:25 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.09 % [INFO] Parsing done (226ms).
% 1.85/1.10 % [INFO] Running in sequential loop mode.
% 2.58/1.31 % [INFO] nitpick registered as external prover.
% 2.58/1.31 % [INFO] Scanning for conjecture ...
% 2.73/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 3.02/1.47 % [INFO] Axiom selection finished. Selected 100 axioms (removed 253 axioms).
% 3.30/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 3.30/1.57 % [INFO] Type checking passed.
% 3.30/1.57 % [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 ...
% 8.35/2.82 % [INFO] Killing All external provers ...
% 8.35/2.82 % Time passed: 2292ms (effective reasoning time: 1719ms)
% 8.35/2.82 % 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)>
% 8.35/2.83 % Axioms used in derivation (2): fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062, conj_0
% 8.35/2.83 % No. of inferences in proof: 20
% 8.35/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2292 ms resp. 1719 ms w/o parsing
% 8.35/2.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.35/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------