TSTP Solution File: SEU706^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 21 03:43:25 EDT 2024
% Result : Theorem 4.68s 2.21s
% Output : Refutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 20 unt; 13 typ; 6 def)
% Number of atoms : 85 ( 47 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 154 ( 15 ~; 6 |; 2 &; 98 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 46 ( 1 ^ 43 !; 2 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(setadjoin__Cong_def,definition,
( setadjoin__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( setadjoin @ A @ C )
= ( setadjoin @ B @ D ) ) ) ) ) ) ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(setunion__Cong_def,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ) ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(setunionsingleton_def,definition,
( setunionsingleton
= ( ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ) ) ) ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(2,negated_conjecture,
~ ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( setadjoin @ A @ C )
= ( setadjoin @ B @ D ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A )
=> ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
in @ sk3 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(8,plain,
( ( setunion @ sk1 )
!= sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
( ( setunion @ sk1 )
!= sk3 ),
inference(lifteq,[status(thm)],[8]) ).
thf(6,plain,
( sk1
= ( setadjoin @ sk2 @ emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
( ( setadjoin @ sk2 @ emptyset )
= sk1 ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ),
inference(cnf,[status(esa)],[3]) ).
thf(21,plain,
! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(22,plain,
! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ),
inference(simp,[status(thm)],[21]) ).
thf(122,plain,
! [A: $i] :
( ( ( setunion @ sk1 )
= A )
| ( ( setadjoin @ sk2 @ emptyset )
!= ( setadjoin @ A @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[14,22]) ).
thf(123,plain,
( ( setunion @ sk1 )
= sk2 ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk2 ))]]) ).
thf(148,plain,
sk3 != sk2,
inference(rewrite,[status(thm)],[23,123]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( B != sk2 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[13,148]) ).
thf(164,plain,
! [A: $i] :
( ~ ( in @ sk3 @ ( setadjoin @ A @ emptyset ) )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( sk3 ))]]) ).
thf(167,plain,
~ ( in @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ),
inference(simp,[status(thm)],[164]) ).
thf(241,plain,
~ ( in @ sk3 @ sk1 ),
inference(rewrite,[status(thm)],[167,14]) ).
thf(242,plain,
$false,
inference(rewrite,[status(thm)],[5,241]) ).
thf(243,plain,
$false,
inference(simp,[status(thm)],[242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 17:37:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.07/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.08 % [INFO] Parsing done (125ms).
% 1.42/1.09 % [INFO] Running in sequential loop mode.
% 1.74/1.33 % [INFO] nitpick registered as external prover.
% 1.88/1.34 % [INFO] Scanning for conjecture ...
% 2.11/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.11/1.44 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.11/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.45 % [INFO] Type checking passed.
% 2.11/1.45 % [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 ...
% 4.68/2.21 % [INFO] Killing All external provers ...
% 4.68/2.21 % Time passed: 1641ms (effective reasoning time: 1118ms)
% 4.68/2.21 % 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)>
% 4.68/2.21 % Axioms used in derivation (0):
% 4.68/2.21 % No. of inferences in proof: 22
% 4.68/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1641 ms resp. 1118 ms w/o parsing
% 4.68/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.68/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------