TSTP Solution File: SET925+1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 03:04:31 EDT 2024
% Result : Theorem 3.53s 2.49s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 19 ( 7 unt; 5 typ; 0 def)
% Number of atoms : 25 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 6 ~; 0 |; 2 &; 49 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^ 14 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(20,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(22,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(19,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(cvc4,[status(thm)],[25,20,17,22,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:14:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.20/1.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.28 % [INFO] Parsing done (171ms).
% 1.49/1.30 % [INFO] Running in sequential loop mode.
% 2.13/1.76 % [INFO] eprover registered as external prover.
% 2.13/1.76 % [INFO] cvc4 registered as external prover.
% 2.13/1.77 % [INFO] Scanning for conjecture ...
% 2.42/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.56/1.91 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.56/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/1.93 % [INFO] Type checking passed.
% 2.56/1.93 % [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 ...
% 3.53/2.48 % External prover 'cvc4' found a proof!
% 3.53/2.49 % [INFO] Killing All external provers ...
% 3.53/2.49 % Time passed: 1963ms (effective reasoning time: 1182ms)
% 3.53/2.49 % 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)>
% 3.53/2.49 % Axioms used in derivation (5): fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, l36_zfmisc_1, antisymmetry_r2_hidden
% 3.53/2.49 % No. of inferences in proof: 14
% 3.53/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1963 ms resp. 1182 ms w/o parsing
% 3.86/2.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------