TSTP Solution File: SET924+1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 2.59s 1.68s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 16 ( 5 unt; 4 typ; 0 def)
% Number of atoms : 23 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 13 ~; 0 |; 2 &; 54 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 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(in_type,type,
in: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(20,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(18,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(16,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,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[20,7,18,16,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 12:29:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (119ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.21 % [INFO] eprover registered as external prover.
% 1.64/1.21 % [INFO] cvc4 registered as external prover.
% 1.64/1.22 % [INFO] Scanning for conjecture ...
% 1.75/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.75/1.29 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.91/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.30 % [INFO] Type checking passed.
% 1.91/1.30 % [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 ...
% 2.59/1.67 % External prover 'e' found a proof!
% 2.59/1.67 % [INFO] Killing All external provers ...
% 2.59/1.68 % Time passed: 1161ms (effective reasoning time: 693ms)
% 2.59/1.68 % 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)>
% 2.59/1.68 % Axioms used in derivation (4): rc2_xboole_0, rc1_xboole_0, antisymmetry_r2_hidden, l34_zfmisc_1
% 2.59/1.68 % No. of inferences in proof: 12
% 2.59/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1161 ms resp. 693 ms w/o parsing
% 2.86/1.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.86/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------