TSTP Solution File: SET917+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET917+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 11:54:50 EDT 2023
% Result : Theorem 2.53s 1.51s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 31 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 94 ( 8 ~; 3 |; 0 &; 75 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 29 !; 4 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_intersection2 @ B @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_intersection2 @ B @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(20,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( disjoint @ ( singleton @ A ) @ B )
| ( ( set_intersection2 @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( disjoint @ ( singleton @ A ) @ B )
| ( ( set_intersection2 @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ( disjoint @ ( singleton @ A ) @ B )
| ( ( set_intersection2 @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(30,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(28,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[25,20,17,11,23,30,15,28,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET917+1 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:11:14 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.94 % [INFO] Parsing done (106ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.48/1.13 % [INFO] eprover registered as external prover.
% 1.48/1.13 % [INFO] cvc4 registered as external prover.
% 1.48/1.14 % [INFO] Scanning for conjecture ...
% 1.67/1.19 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.75/1.21 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.75/1.22 % [INFO] Problem is first-order (TPTP FOF).
% 1.75/1.22 % [INFO] Type checking passed.
% 1.75/1.22 % [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 ...
% 2.53/1.51 % External prover 'e' found a proof!
% 2.53/1.51 % [INFO] Killing All external provers ...
% 2.53/1.51 % Time passed: 999ms (effective reasoning time: 558ms)
% 2.53/1.51 % 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)>
% 2.53/1.51 % Axioms used in derivation (8): idempotence_k3_xboole_0, commutativity_k3_xboole_0, l28_zfmisc_1, l32_zfmisc_1, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 2.53/1.51 % No. of inferences in proof: 20
% 2.53/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 999 ms resp. 558 ms w/o parsing
% 2.76/1.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.76/1.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------