TSTP Solution File: SET978+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:54:58 EDT 2023
% Result : Theorem 2.74s 1.65s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 18 ( 5 unt; 4 typ; 0 def)
% Number of atoms : 28 ( 5 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 111 ( 9 ~; 2 |; 3 &; 88 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 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 : 32 ( 0 ^; 28 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(20,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( disjoint @ ( cartesian_product2 @ ( singleton @ A ) @ C ) @ ( cartesian_product2 @ ( singleton @ B ) @ D ) )
& ( disjoint @ ( cartesian_product2 @ C @ ( singleton @ A ) ) @ ( cartesian_product2 @ D @ ( singleton @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(15,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[20,13,18,23,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n021.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 : Thu May 18 18:45:58 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.00/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.04 % [INFO] Parsing done (121ms).
% 1.31/1.05 % [INFO] Running in sequential loop mode.
% 1.70/1.24 % [INFO] eprover registered as external prover.
% 1.70/1.25 % [INFO] cvc4 registered as external prover.
% 1.70/1.25 % [INFO] Scanning for conjecture ...
% 1.91/1.30 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.91/1.33 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.91/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.34 % [INFO] Type checking passed.
% 1.91/1.34 % [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 ...
% 2.74/1.65 % External prover 'e' found a proof!
% 2.74/1.65 % [INFO] Killing All external provers ...
% 2.74/1.65 % Time passed: 1114ms (effective reasoning time: 596ms)
% 2.74/1.65 % 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)>
% 2.74/1.65 % Axioms used in derivation (5): t17_zfmisc_1, symmetry_r1_xboole_0, rc2_xboole_0, t127_zfmisc_1, rc1_xboole_0
% 2.74/1.65 % No. of inferences in proof: 14
% 2.74/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1114 ms resp. 596 ms w/o parsing
% 2.74/1.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.74/1.68 % [INFO] Killing All external provers ...
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