TSTP Solution File: SET899+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET899+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 03:07:18 EDT 2024
% Result : Theorem 4.29s 2.38s
% Output : Refutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 37 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 129 ( 10 ~; 13 |; 0 &; 99 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 ^ 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
~ ( subset @ sk1 @ ( set_difference @ sk2 @ ( singleton @ sk3 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( in @ C @ A )
| ( ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) )
!= ( subset @ sk1 @ ( set_difference @ sk2 @ ( singleton @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,10]) ).
thf(37,plain,
( ~ ( subset @ sk1 @ sk2 )
| ( in @ sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(11,plain,
~ ( in @ sk3 @ sk1 ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
subset @ sk1 @ sk2,
inference(cnf,[status(esa)],[9]) ).
thf(56,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[37,11,12]) ).
thf(57,plain,
$false,
inference(simp,[status(thm)],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET899+1 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 11:33:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.99/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.11 % [INFO] Parsing done (156ms).
% 1.26/1.13 % [INFO] Running in sequential loop mode.
% 1.87/1.49 % [INFO] nitpick registered as external prover.
% 1.87/1.50 % [INFO] Scanning for conjecture ...
% 2.02/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.02/1.63 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.17/1.64 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.64 % [INFO] Type checking passed.
% 2.17/1.65 % [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 ...
% 4.29/2.37 % [INFO] Killing All external provers ...
% 4.29/2.38 % Time passed: 1907ms (effective reasoning time: 1240ms)
% 4.29/2.38 % 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)>
% 4.29/2.38 % Axioms used in derivation (1): l3_zfmisc_1
% 4.29/2.38 % No. of inferences in proof: 15
% 4.29/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1907 ms resp. 1240 ms w/o parsing
% 4.29/2.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.29/2.42 % [INFO] Killing All external provers ...
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