TSTP Solution File: SET936+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET936+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 11:54:53 EDT 2023
% Result : Theorem 74.28s 13.19s
% Output : Refutation 74.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 33 ( 16 unt; 5 typ; 0 def)
% Number of atoms : 71 ( 15 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 205 ( 6 ~; 0 |; 16 &; 156 @)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 62 ( 0 ^; 58 !; 4 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(powerset_type,type,
powerset: $i > $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(69,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(74,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(85,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(77,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(81,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( B
= ( powerset @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(79,plain,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( powerset @ ( set_intersection2 @ A @ B ) )
= ( set_intersection2 @ ( powerset @ A ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( powerset @ ( set_intersection2 @ A @ B ) )
= ( set_intersection2 @ ( powerset @ A ) @ ( powerset @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( powerset @ ( set_intersection2 @ A @ B ) )
= ( set_intersection2 @ ( powerset @ A ) @ ( powerset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(72,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_intersection2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37062,plain,
$false,
inference(cvc4,[status(thm)],[69,20,74,85,77,81,18,23,79,15,83,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET936+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu May 18 19:02:28 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.87/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (143ms).
% 1.17/0.97 % [INFO] Running in sequential loop mode.
% 1.63/1.19 % [INFO] eprover registered as external prover.
% 1.63/1.20 % [INFO] cvc4 registered as external prover.
% 1.63/1.20 % [INFO] Scanning for conjecture ...
% 1.80/1.26 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.80/1.28 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.80/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.80/1.31 % [INFO] Type checking passed.
% 1.80/1.31 % [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 ...
% 74.28/13.19 % External prover 'cvc4' found a proof!
% 74.28/13.19 % [INFO] Killing All external provers ...
% 74.28/13.19 % Time passed: 12702ms (effective reasoning time: 12220ms)
% 74.28/13.19 % 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)>
% 74.28/13.19 % Axioms used in derivation (12): idempotence_k3_xboole_0, commutativity_k3_xboole_0, t1_xboole_1, t2_tarski, d1_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0, t19_xboole_1, t17_xboole_1, d3_xboole_0, antisymmetry_r2_hidden
% 74.28/13.19 % No. of inferences in proof: 28
% 74.28/13.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12702 ms resp. 12220 ms w/o parsing
% 74.28/13.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 74.28/13.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------